1. A cloaking mechanism: The TARDIS is famous for its so-called chameleon circuit, which is supposed to ensure that the exterior of the ship always fits in with the surrounding environment - except this particular circuit is faulty; it got stuck in the blue police box form after visiting London in 1963, and it's been a blue police box ever since.
We're in luck on this score: There are any number of cutting-edge cloaking technologies being developed by scientists; one of them is bound to work for our purposes.
2. Biometric security system: Before a TARDIS can be fully functional, it has to receive the "biological imprint" of a Time Lord, via the "Rassilon Imprimatur." The series is rather vague on the details, but it's got something to do with the biological makeup of Time Lords. But the point is to make sure a TARDIS isn't misused. Fortunately, biometrics for confirming identity have been around for ages. Piece of cake.
3. Extra dimensions: Everyone knows the TARDIS is bigger on the inside; I believe the technical term is "dimensionally transcendental," that is, the exterior and interior exist in separate dimensions. Or something. Now we're getting into more difficult territory, because while the possibility of extra dimensions of space has been theorized in great mathematical detail, not even the Large Hadron Collider has yet to find any experimental verification of their existence.
Still, if we assume that string theory is correct in its assertion that we just can't see those extra dimensions because they're all curled up in tiny Calabi-Yau shapes at the Planck scale, I'm willing to postulate that the Doctor's TARDIS has found a way to exploit that feature for practical purposes. I just don't know how we're going to go about following suit.
4. A black hole: Every time machine needs a power source. Or two. One of the power sources for the TARDIS is the singularity of a black hole - an artificial black hole called The Eye of Harmony. One assumes it's located near the Doctor's home planet of Gallifrey (but not too close!).
While the LHC has yet to create mini-black holes - despite a lot of hysteria a few years ago on just that score - I suppose we could substitute the singularity of the black hole at the center of our own Milky Way galaxy. We just need to figure out how to harness that energy.
5. Teleportation: The dematerializing and rematerializing hint that the TARDIS exploits some form of teleportation. We already can teleport tiny particles, if not a big blue police box. Give us another couple of decades, and we'll have this teleportation thing down. (Just call me Olive Overly-Optimistic!) But we probably also need ...
6. A wormhole: The opening credit sequence always shows the Tardis whipping through the "time vortex," which looks for all the world like a wormhole. Apparently it dematerializes, goes through the time vortex and rematerializes at its destination.
A wormhole is basically a black hole with an opening punched through the center that connects two separate areas of spacetime. But it's not something we'll just find lying around the universe. Among the things you'd need to create a transversable wormhole: negative energy.
Sure, the Doctor can build a wormhole any time he likes, because he's got access to fancy fictional things like "artron energy," apparently some form of temporal energy that emanates from the minds of Time Lords. (The TARDIS itself boasts "huon energy." It's so much easier when you can just make this stuff up.)
Many a science fiction fan has speculated about the possibility of harnessing the vacuum energy for this purpose. It's sufficient, it seems, to make the expansion of the universe accelerate (according to the current favored theory among physicists), but practical wormhole applications won't transpire anytime soon. Alas.
7. A trachoid time crystal: Any machine has lots of moving parts, and the TARDIS is no different. One of those parts, mentioned in the "Doctor Who" serial "The Hand of Fear," from 1976, is a trachoid time crystal.
Oh, come on! Does such a thing even exist? Well, according to Nobel Prize-winning physicist Frank Wilczek, something like it just might be possible - mathematically, at least. He was teaching a class on 3-D crystals and started wondering whether you could have a crystal-like structure in the fourth dimension of time - i.e., a time crystal. A couple of scientific papers later, he concluded that, indeed, you could.
As Alexandra Witze explains in Science News:
To visualize a time crystal, think of Earth looping back to its same location in space every 365¼ days; the planet repeats itself periodically as it moves through time. But a true time crystal is made not of a planet but of an object in its lowest energy state, like an electron stripped of all possible energy.
Witze goes on to compare the "time crystal" to a perpetual motion machine that doesn't defy the laws of thermodynamics, because it's already in its lowest energy state; hence, no work can be extracted from the system. If Wilczek has a found a way to beat the Second Law of Thermodynamics, we should just go ahead and make him the next Doctor. I'm sure Matt Smith wouldn't mind.
Images: Top: The Time Lords' vehicle of choice. Credit: Corbis. Middle: Architectural rendering of a TARDIS blueprint by Sherrod Drawings. Source.